*POSSIBLE MISSION SPOILERS*
BRIEFING:
High Overseer Campbell leads the city's militant religious faction and is a close ally to the Lord Regent. Campbell is completely corrupt and holds the secret to Emily's location. Infiltrate the Office of the High Overseer, steal Campbell's journal and eliminate him. An ally to the Loyalists, Martin, is being held there. Free him and allow him to escape.
IGN shows you how to get through mission two of Dishonored without killing anyone or being detected. Completing the game in this fashion earns you the 'Ghost,' 'Shadow,' and 'Clean Hands' trophies / achievements.